Zwelinzima Vavi.
Demands Zwelinzima Vavi to be reinstated undermine Cosatu's internal processes, it said on Tuesday.
"Cosatu will not allow that to happen," said acting general secretary Bheki Ntshalintshali.
He said Vavi had been suspended for violating Cosatu's code of conduct.
"The general secretary is not above the law of Cosatu. He, like anyone else, has a responsibility to come before the disciplinary process and clear his name."
He said Vavi had gone public and admitted to having violated the code of conduct.
"He made these admissions freely and voluntarily, when he was in his sound and sober senses, without being unduly influenced."
Ntshalintshali said an investigation was conducted, and that charges were formulated based on the finding of the investigation.
Numsa
The National Union of Metalworkers of South Africa (Numsa) wants the ANC to lose the election, Cosatu said on Tuesday.
"This cannot be done in the name of Cosatu," Ntshalintshali told reporters.
He said Numsa leadership was pursuing an agenda aimed at destroying the Cosatu, the ANC and the South African Communist Party.
This programme was aimed at ensuring Cosatu was weakened and was calculated to ensure the ANC lost the election, and that the SACP was also liquidated "so that all these formation can be replaced by the Numsa and its allies", he said.
Ntshalintshali said that as long as Numsa was a Cosatu affiliate it had to abide by its constitution and policies.
At a special national congress in December, Numsa resolved that it would not support the ANC in the May 7 national election, and would also not fund the ANC's election campaign.
Cosatu is in an alliance with the ANC and the SACP.
Numsa has also called on Cosatu to break away from the alliance. – Sapa